Abstract

This work considers the cooperative trajectory-planning problem along a double lane change scenario for autonomous driving. In this paper, we develop two frameworks to solve this problem based on distributed model predictive control (MPC). The first approach solves a single nonlinear MPC problem. The general idea is to introduce a collision cost function in the optimization problem at the planning task to achieve a smooth and bounded collision function, and thus to prevent the need to implement tight hard constraints. The second method uses a hierarchical scheme with two main units: a trajectory-planning layer based on mixed-integer quadratic program (MIQP) computes an on-line collision-free trajectory using simplified motion dynamics, and a tracking controller unit to follow the trajectory from the higher level using the nonlinear vehicle model. Connected and automated vehicles (CAVs) sharing their planned trajectories lay the foundation of the cooperative behavior. In the tests and evaluation of the proposed methodologies, matlab-carsim cosimulation is utilized. carsim provides the high-fidelity model for the multibody vehicle dynamics. matlab-carsim conjoint simulation experiments compare both approaches for a cooperative double lane change maneuver of two vehicles moving along a one-way three-lane road with obstacles.

References

1.
Geiger
,
A.
,
Lenz
,
P.
, and
Urtasun
,
R.
,
2012
, “
Are We Ready for Autonomous Driving? The Kitti Vision Benchmark Suite
,”
IEEE Conference on Computer Vision and Pattern Recognition
, Providence, RI, June 16–21, pp.
3354
3361
.10.1109/CVPR.2012.6248074
2.
Yuan
,
H.
,
Sun
,
X.
, and
Gordon
,
T.
,
2019
, “
Unified Decision-Making and Control for Highway Collision Avoidance Using Active Front Steer and Individual Wheel Torque Control
,”
Veh. Syst. Dyn.
,
57
(
8
), pp.
1188
1118
.10.1080/00423114.2018.1535125
3.
Kelly
,
A.
, and
Nagy
,
B.
,
2003
, “
Reactive Nonholonomic Trajectory Generation Via Parametric Optimal Control
,”
Int J Rob Res.
,
22
(
7–8
), pp.
583
601
.10.1177/02783649030227008
4.
Hassanzadeh
,
M.
,
Lidberg
,
M.
, and
Keshavarz
,
M.
,
Bjelkeflo
,
L.
,
2012
, “
Path and Speed Control of a Heavy Vehicle for Collision Avoidance Manoeuvres
,”
IEEE Intelligent Vehicles Symposium (IV)
,
Alcala de Henares, Spain, June 3–7, pp. 129–134
.10.1109/IVS.2012.6232254
5.
Sichitiu
,
M. L.
, and
Kihl
,
M.
,
2008
, “
Inter-Vehicle Communication Systems: A Survey
,”
IEEE Commun. Surv. Tutorials
,
10
(
2
), pp.
88
105
.10.1109/COMST.2008.4564481
6.
Schouwenaars
,
T.
,
Demoor
,
B.
,
Feron
,
E.
,
How
,
J.
,
2001
, “
Mixed Integer Programming for Multi-Vehicle Path Planning
,”
Proceedings European Control Conference
, Porto, Portugal, Sept. 4–7, pp.
2603
2608
.10.23919/ECC.2001.7076321
7.
Frese
,
C.
, and
Beyerer
,
J.
,
2011
, “
A Comparison of Motion Planning Algorithms for Cooperative Collision Avoidance of Multiple Cognitive Automobiles
,”
IEEE Intelligent Vehicles Symposium (IV)
, Baden-Baden, Germany, June 5–9, pp.
1156
1162
.10.1109/IVS.2011.5940489
8.
Wang
,
D.
,
Hu
,
M.
,
Wang
,
Y.
,
Wang
,
J.
,
Qin
,
H.
, and
Bian
,
Y.
,
2016
, “
Model Predictive Control-Based Cooperative Lane Change Strategy for Improving Traffic Flow
,”
Adv. Mech. Eng.
,
8
(
2
), pp.
1
17
.10.1177/1687814016632992
9.
Viana
,
B.
, and
Aouf
,
N.
,
2018
, “
Distributed Cooperative Path-Planning for Autonomous Vehicles Integrating Human Driver Trajectories
,”
International Conference on Intelligent Systems (is)
, Madeira Island, Portugal, Sept. 25–27, pp.
655
661
.10.1109/IS.2018.8710544
10.
Viana
,
B.
,
Kanchwala
,
H.
, and
Aouf
,
N.
,
2019
, “
Cooperative Trajectory Planning for Autonomous Driving Using Nonlinear Model Predictive Control
,” IEEE International Conference on Connected Vehicles and Expo (
ICCVE
), Graz, Austria, Nov. 4–8, pp.
1
6
.10.1109/ICCVE45908.2019.8965227
11.
Zeilinger
,
M. N.
,
Morari
,
M.
, and
Jones
,
C. N.
,
2014
, “
Soft Constrained Model Predictive Control With Robust Stability Guarantees
,”
IEEE Trans. Autom. Control
,
59
(
5
), pp.
1190
1202
.10.1109/TAC.2014.2304371
12.
Kuriki
,
Y.
, and
Namerikawa
,
T.
,
2015
, “
Formation Control With Collision Avoidance for a Multi-UAV System Using Decentralized Mpc and Consensus-Based Control
,”
SICE J. Control, Meas., Syst. Integr.
,
8
(
4
), pp.
285
294
.10.9746/jcmsi.8.285
13.
Ji
,
J.
,
Khajepour
,
A.
,
Melek
,
W. W.
, and
Huang
,
Y.
,
2017
, “
Path Planning and Tracking for Vehicle Collision Avoidance Based on Model Predictive Control With Multiconstraints
,”
IEEE Trans. Veh. Technol.
,
66
(
2
), pp.
952
964
.10.1109/TVT.2016.2555853
14.
Shibata
,
N.
,
Sugiyama
,
S.
, and
Wada
,
T.
,
2014
, “
Collision Avoidance Control With Steering Using Velocity Potential Field
,”
IEEE Intelligent Vehicles Symposium Proceedings
, Dearborn, MI, June 8–11, pp.
438
443
.10.1109/IVS.2014.6856469
15.
You
,
F.
,
Zhang
,
R.
,
Lie
,
G.
,
Wang
,
H.
,
Wen
,
H.
, and
Xu
,
J.
,
2015
, “
Trajectory Planning and Tracking Control for Autonomous Lane Change Maneuver Based on the Cooperative Vehicle Infrastructure System
,”
Expert Syst. Appl.
,
42
(
14
), pp.
5932
5946
.10.1016/j.eswa.2015.03.022
16.
Nilsson
,
J.
, and
Sjberg
,
J.
,
2013
, “
Strategic Decision Making for Automated Driving on Two-Lane, One Way Roads Using Model Predictive Control
,”
IEEE Intelligent Vehicles Symposium (IV)
, Gold Coast, Australia, June 23–26, pp.
1253
1258
.10.1109/IVS.2013.6629638
17.
Schildbach
,
G.
, and
Borrelli
,
F.
,
2015
, “
Scenario Model Predictive Control for Lane Change Assistance on Highways
,”
IEEE Intelligent Vehicles Symposium (IV)
, Seoul, South Korea, June 28-July 1, pp.
611
616
.10.1109/IVS.2015.7225752
18.
Quinlan
,
S.
, and
Khatib
,
O.
,
1993
, “
Elastic Bands: Connecting Path Planning and Control
,”
IEEE International Conference on Robotics and Automation
, Vol.
2
, Atlanta, GA, May 2–6, pp.
802
807
.10.1109/ROBOT.1993.291936
19.
Hilgert
,
J.
,
Hirsch
,
K.
,
Bertram
,
T.
, and
Hiller
,
M.
,
2003
, “
Emergency Path Planning for Autonomous Vehicles Using Elastic Band Theory
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
(
AIM 2003
), Vol.
2
, Kobe, Japan, July 20–24, pp.
1390
1395
.10.1109/AIM.2003.1225546
20.
Gehrig
,
S. K.
, and
Stein
,
F. J.
,
2007
, “
Collision Avoidance for Vehicle-Following Systems
,”
IEEE Trans. Intell. Transport. Syst.
,
8
(
2
), pp.
233
244
.10.1109/TITS.2006.888594
21.
Kala
,
R.
, and
Warwick
,
K.
,
2013
, “
Planning Autonomous Vehicles in the Absence of Speed Lanes Using an Elastic Strip
,”
IEEE Trans. Intell. Transport. Syst.
,
14
(
4
), pp.
1743
1752
.10.1109/TITS.2013.2266355
22.
Lenz
,
D.
,
Kessler
,
T.
, and
Knoll
,
A.
,
2016
, “
Tactical Cooperative Planning for Autonomous Highway Driving Using Monte Carlo Tree Search
,”
IEEE Intelligent Vehicles Symposium (IV)
, Gothenburg, Sweden, June 19–22,
pp.
447
453
.10.1109/IVS.2016.7535424
23.
Kurzer
,
K.
,
Engelhorn
,
F.
, and
Zllner
,
J. M.
,
2018
, “
Decentralized Cooperative Planning for Automated Vehicles With Continuous Monte Carlo Tree Search
,” 21st International Conference on Intelligent Transportation Systems (
ITSC
), Changshu, China, June 26–30, pp.
452
459
.https://www.researchgate.net/publication/327552119_Decentralized_Cooperative_Planning_for_Automated_Vehicles_with_Continuous_Monte_Carlo_Tree_Search
24.
Venkatraman
,
A.
, and
Bhat
,
S. P.
,
2006
, “
Optimal Planar Turns Under Acceleration Constraints
,”
45th IEEE Conference Decision Control
, San Diego, CA, Dec. 13–15, pp.
235
240
.10.1109/CDC.2006.377809
25.
Shamir
,
T.
,
2004
, “
How Should an Autonomous Vehicle Overtake a Slower Moving Vehicle: Design and Analysis of an Optimal Trajectory
,”
IEEE Trans. Autom. Control
,
49
(
4
), pp.
607
610
.10.1109/TAC.2004.825632
26.
Anisi
,
D. A.
,
Hamberg
,
J.
, and
Hu
,
X.
,
2003
, “
Nearly Time-Optimal Paths for a Ground Vehicle
,”
J. Control Theory Appl.
,
1
(
1
), pp.
2
8
.10.1007/s11768-003-0002-6
27.
Dingle
,
P.
, and
Guzzella
,
L.
,
2010
, “
Optimal Emergency Maneuvers on Highways for Passenger Vehicles With Two- and Four-Wheel Active Steering
,”
American Control Conference
, Baltimore, MD, June 30–July 2, pp.
5374
5381
.10.1109/ACC.2010.5530760
28.
Tomas-Gabarron
,
J.-B.
,
Egea-Lopez
,
E.
, and
Garcia-Haro
,
J.
,
2011
, “
Evaluating Communications and Idm in a Context of Chain Cca Application for Vanets
,”
Third International Conference on Road Safety and Simulation Purdue University Transportation Research Board
, Indianapolis, IN, Sept. 14–16.
29.
Tomas-Gabarron
,
J.
,
Egea-Lopez
,
E.
, and
Garcia-Haro
,
J.
,
2013
, “
Vehicular Trajectory Optimization for Cooperative Collision Avoidance at High Speeds
,”
IEEE Trans. Intell. Transport. Syst.
,
14
(
4
), pp.
1930
1941
.10.1109/TITS.2013.2270009
30.
Eilbrecht
,
J.
, and
Stursberg
,
O.
,
2019
, “
Reducing Computation Times for Planning of Reference Trajectories in Cooperative Autonomous Driving
,”
IEEE Intelligent Vehicles Symposium (IV)
, Paris, France, June 9–12, 146–152.10.1109/IVS.2019.8814266
31.
Burger
,
C.
, and
Lauer
,
M.
,
2018
, “
Cooperative Multiple Vehicle Trajectory Planning Using MIQP
,” 21st International Conference on Intelligent Transportation Systems (
ITSC
), Maui, HI, Nov. 4–7, pp.
602
607
.10.1109/ITSC.2018.8569776
32.
Salvado
,
J.
,
Krug
,
R.
,
Mansouri
,
M.
, and
Pecora
,
F.
,
2018
, “
Motion Planning and Goal Assignment for Robot Fleets Using Trajectory Optimization
,” IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
), Madrid, Spain, Oct. 1–5, pp.
7939
7946
.https://www.researchgate.net/publication/330245103_Motion_Planning_and_Goal_Assignment_for_Robot_Fleets_Using_Trajectory_Optimization
33.
Branca
,
C.
, and
Fierro
,
R.
,
2006
, “
A Hierarchical Optimization Algorithm for Cooperative Vehicle Networks
,”
American Control Conference
, Minneapolis, MN, June 14–16, pp.
4225
4230
.
34.
Miller
,
C.
,
Pek
,
C.
, and
Althoff
,
M.
,
2018
, “
Efficient Mixed-Integer Programming for Longitudinal and Lateral Motion Planning of Autonomous Vehicles
,”
IEEE Intelligent Vehicles Symposium (IV)
, Changshu, China, June 26–30, pp.
1954
1961
.10.1109/IVS.2018.8500394
35.
Pacejka
,
H.
,
2005
,
Tire and Vehicle Dynamics
,
Elsevier
, Amsterdam, The Netherlands.
36.
Rajamani
,
R.
,
2012
,
Vehicle Dynamics and Control
,
Springer
, New York.
37.
Zhang
,
K.
,
Sprinkle
,
J.
, and
Sanfelice
,
R. G.
,
2015
, “
A Hybrid Model Predictive Controller for Path Planning and Path Following
,” Proceedings of the ACM/IEEE Sixth International Conference on Cyber-Physical Systems (
ICCPS '15
), ACM, Seattle, WA, Apr. 14–16, pp.
139
148
.10.1145/2735960.2735966
38.
Westfield, “
Sports Cars
,”
Westfield,
accessed July 22,
2020
, https://westfield-sportscars.co.uk
39.
MuCCA, "Multi-Car Collision Avoidance Project,”
MuCCA
, accessed Mar. 20, 2020, http://mucca-project.co.uk
40.
Kanchwala
,
H.
,
Viana
,
I. B.
, and
N
,
A.
,
2020
, “
Cooperative Path-Planning and Tracking Controller Evaluation Using Vehicle Models of Varying Complexities
,”
Proc. Inst. Mech. Eng., Part C
, epub.10.1177/0954406220945468
41.
Eckelmann
,
S.
,
Trautmann
,
T.
,
Ußler
,
H.
,
Reichelt
,
B.
, and
Michler
,
O.
,
2017
, “
V2v-Communication, Lidar System and Positioning Sensors for Future Fusion Algorithms in Connected Vehicles
,”
Transport. Res. Procedia
,
27
, pp.
69
76
.10.1016/j.trpro.2017.12.032
42.
Williams
,
H. P.
, and
Brailsford
,
S. C.
,
1996
,
Computational Logic and Integer Programming
,
J. E.
Beasley
, ed.,
Oxford University Press
, Oxford, UK.
43.
IBM
,
2009
, “
IBM ILOG CPLEX V12.1: User's Manual for CPLEX
,” IBM.
44.
Wartnaby
,
C. E.
,
Nam
,
D.
, and
Viana
,
I. B.
,
2018
, “
Multi-Car Collision Avoidance
,”
ITS World Congress
, Copenhagen, Denmark, Sept. 17–21.
45.
Mechanical Simulation Corporation
,
2016
, “
CarSim User Reference Manual
,” Mechanical Simulation Corporation.
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